Cumulant microscopy

ABSTRACT

The invention describes a method and a microscopy system for imaging and analysing stochastically and independently blinking point-like emitters. A multiple-order cumulants analysis in conjunction with an established blinking model enables the extraction of super-resolved environment-related parameter maps, such as molecular state lifetimes, concentration and brightness distributions of the emitter. In addition, such parameter maps can be used to compensate for the non-linear brightness and blinking response of higher-order cumulant images—used for example in Super-resolution Optical Fluctuation Imaging (SOFI)—to generate a balanced image contrast. Structures that otherwise would be masked by brighter regions in the conventional cumulant image become samples using spectral cross-cumulants.

FIELD OF THE INVENTION

The present invention relates to the field of super-resolutionmicroscopy, and in particular to an improved method based onmultiple-order cumulants analysis of the blinking behaviour ofindividual point-like emitters.

STATE OF THE ART

The references describe the background of the invention and are herebyincorporated.

The spatial resolution in optical microscopes is limited by diffraction.This so-called Abbe limit according to Abbe's theory of opticalmicroscopy and image formation restricts the optical resolution. In thistheory of image formation no further information is known of the objectto be investigated. However, if object properties are known, as influorescence microscopy, where the fluorescent labels are emitting lightin a known statistical manner, with an emitter size well below thediffraction limit, a higher resolution can be achieved by exploitingsaturation effects or utilizing stochastic blinking to identify andlocalize single emitters. These new imaging concepts are known assuper-resolution microscopy.

During the last two decades, several new imaging concepts overcoming thediffraction limit have been disclosed and filed:

STED as described for example in the U.S. Pat. No. 5,731,588, U.S. Pat.No. 7,719,679, U.S. Pat. No. 7,538,893, U.S. Pat. No. 7,430,045, U.S.Pat. No. 7,253,893, U.S. Pat. No. 7,064,824 with the demand for aspecial optical imaging instrumentation, a limited acquisition timemainly due to the known limitations of an image scanning device and therequirement for strong excitation sources in order to achievesuper-resolution with a good imaging contrast.

SIM; SSIM; I5M; as described for example in the U.S. Pat. No. 5,671,085with a demonstrated super-resolution due to structured illuminationbased on a rather complicated optical setup and the necessity to extractthe improved resolution by combining several images acquired with aphase controlled illumination sequence.

PALM as well as STORM as described for example in the U.S. Pat. No.7,710,563, U.S. Pat. No. 7,626,703, U.S. Pat. No. 7,626,695, U.S. Pat.No. 7,626,694, U.S. Pat. No. 7,535,012 are based on a widefieldfluorescence microscopy concept exploiting the stochastic blinking ofindividual fluorophores. These methods impose stringent requirements onthe labeling density along with meta-stable dark-states of thefluorophores versus high brightness in the fluorescent state. Bothmethods require rather long acquisition times for recording thousands ofimages. However, illumination or sample induced stochastic switching offluorophores followed by localization proved to be an innovative conceptwith a substantial resolution enhancement demonstrated fortwo-dimensional (2D) images. Three-dimensional (3D) localizationmicroscopy usually needs a modification of the optical setup.Furthermore, many of the proposed solutions are suffering from a ratherlimited depth of field and are limited due to background radiationoriginating from unresolved and out-of-focus sample structures.

Lidke et al. published in 2005 (Optics Express 2005, Vol. 13, pp.7052-7062) a novel imaging concept based on Independent ComponentAnalysis (ICA) and the blinking statistics of quantum dots (QDs)allowing for the separation and localization of overlapping diffractionpatterns. However, for a successful localization, an estimation of thenumber of QDs is needed and the position accuracy is substantiallyinfluenced by an under- or overestimation of the number of emitters.

SOFI as described in the patent PCT/US2010/037099 represents a newsuper-resolved imaging concept, which exploits the statistical blinkingbehaviour of the fluorescent biomarkers without any prior knowledge ofemitters within a diffraction-limited spot. SOFI is based on apixel-wise auto- or cross-cumulant analysis, which yields a resolutionenhancement that grows with the cumulant order in all three dimensions.Uncorrelated noise, stationary background as well as out-of-focus lightare greatly reduced by the cumulant analysis. Hence, the step from two-to three-dimensional imaging is facilitated and can be easily realizedin a so-called z-stacking, i.e. the sequential imaging of depth slices,well known in classical and confocal microscopy. 2D and 3D imaging canbe performed with a classical widefield or confocal microscope.Acquiring multiple image sequences of blinking fluorophores and applyingthe pixel-wise cumulant analysis in a post processing is sufficient togenerate super-resolved 3D images. The main drawback of SOFI is theamplification of heterogeneities in molecular brightness andphoto-kinetics, which limits the use of higher-order cumulants.

At the exception of STED, all mentioned super-resolution techniquesprovide structural information only. The blinking behaviour is notevaluated further even though it might provide physically meaningfulparameters that may be linked to microenvironment properties and therebyreport functional information.

There is still an important need for an imaging concept providingsuper-resolution along with functional information, high contrast, apotential for fast imaging, intrinsic 3D capability, live-cellsuitability, and compatibility with commercially available microscopes.

GENERAL DESCRIPTION OF THE INVENTION

An objective of the invention is to solve at least the above-mentionedproblems and/or disadvantages and to provide the advantages describedherewith in the following.

The invention aims to use higher-order statistics for characterizing theblinking kinetics of single point-like emitters and estimate the spatialdistribution of molecular brightness and density to extractmicroenvironment-related properties with super-resolution.

Another objective of the invention is to correct for the resultingbrightness imbalance of cumulant-based super-resolution yielding animproved contrast and revealing hidden structural information.

Further on, the invention describes the possibility of combining thecomplementary cumulant- and localization-based super-resolutiontechniques to increase their applicability and overall performance.

Another objective is to expand the range of suitable probes forblinking-based super-resolution microscopy by the use ofillumination-induced fluctuations with a (saturated) structuredexcitation such as a speckle field, or the use of a modulated excitationalong with synchronized detection to populate and sense the fast tripletstate fluctuations.

Another objective is to perform super-resolved multi-colour,colocalization, FRET and anisotropy analysis by using cross-cumulants indifferent spectral and/or polarization channels.

The above-cited objectives are achieved with the present invention,which concerns a method and a microscopy system as defined in theclaims.

Additional advantages, objects and features of the invention will be setforth in the following chapters.

DEFINITIONS, TERMS AND ELEMENTS

“Point-like emitter”: Small particle (with respect to the point-spreadfunction) that absorbs, reemits or scatters photons.

“Stochastic blinking”: A fluctuation in measurable optical properties(e.g. emission, absorption or scattering) between at least two states ofthe point-like emitter. It can be intrinsic or provoked by externalmeans and has to be independent among the individual emitters. Forexample, the fluctuation can be caused by a transition between two ormore molecular energy levels or by a reorientation or conformationalchange.

“Parameter map”: Image or volume rendering encoding the spatialdistribution of an estimated physical quantity.

“Microenvironment”: Local concentration of a certain molecular speciesor the strength of a property of the medium in vicinity to a point-likeemitter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1: Data acquisition

FIG. 2: Cumulants computation

FIG. 3: Flowchart for obtaining the super-resolved spatial distributionof photo-physical parameters

FIG. 4: Flowchart for obtaining balanced cumulants

FIG. 5: Illustration of balanced cumulants in comparison to unbalancedcumulants

FIG. 6: Modulated excitation and synchronized detection scheme fortriplet cumulant microscopy

FIG. 7: Example wide-field implementation of triplet cumulant microscopy

FIG. 8: Flowchart for hardware implementation

FIG. 9: Multi-plane detection scheme

FIG. 10: Example of fourth-order 3D cross-cumulant pixel combinationswithout repetitions

FIG. 11: Example detection scheme for multi-colour cumulant microscopy

DETAILED DESCRIPTION OF THE INVENTION

The present invention describes a method for imaging and analysing afield-of-view composed of stochastically and independently blinkingpoint-like emitters.

The acquisition procedure and the hardware requirements are similar tothose described in the SOFI patent PCT/US2010/037099. An optical imagingsystem (microscope, telescope, etc.) is used to acquire the abovementioned field-of-view repeatedly (over time) in wide-field or confocaldetection. The blinking signals emanating from individual point-likeemitters are blurred by the point-spread function (PSF, impulseresponse) of the optical system and recorded on a set of detectionelements (pixels) as a function of time. The extent of the PSF shallonly be limited by diffraction and optical aberrations in the detectionarm. Therefore, the PSF shall spread over several pixels. Theinstrumentation has to be suited and sensitive enough to detect thestochastic blinking of the emitter in time and space.

FIG. 1 shows schematically the signal acquisition process in wide-fielddetection. The system is subdivided in the sample space 10, themicroscope system 20 (schematically) and the detector space 30containing an array detector 31. The sample space 10 shows a selected 2Dsample plane 11, containing several point-like emitters 12 located insaid sample plane 11. The microscope system 20, represented by theimaging elements 21, provides images of point-like emitters inside thefield of view 13. In general the microscope system 20 can only accesspoint-like emitters, which are emitting light (14, 15). The distancebetween the emitters 14, 15 is below the resolution limit set by the PSFsize. Therefore the corresponding images 34, 35 captured by the arraydetector 31 show overlapping unresolved blurred spots. A time series ofcaptured and memorized images 41 contains the data corresponding to thecaptured images/spots of the stochastically blinking point-likeemitters. The memory buffer 40 contains sufficiently long registereddata sets used for the following cumulant analysis.

Similarly to SOFI, the acquired pixel time traces are extracted andprocessed by calculating higher-order (cross-) cumulants, with orwithout time lags. In the most general sense, the cumulant of order n ofa pixel set P={{right arrow over (p)}₁, {right arrow over (p)}₂, . . . ,{right arrow over (p)}_(n)} with time lags {right arrow over (τ)}=[τ₁,τ₂, . . . , τ_(n)] can be calculated according to Leonov and Shiryaef(Theory Probab. Appl. (1959) vol. 4 (3) pp. 319-329) as

${{\kappa_{n}\left( {{\overset{\rightarrow}{p} = {\frac{1}{n}{\sum\limits_{i = 1}^{n}{\overset{\rightarrow}{p}}_{i}}}};\tau} \right)} = {\sum\limits_{s}^{\;}{\left( {- 1} \right)^{q_{s} - 1}{\left( {q_{s} - 1} \right)!}{\prod\limits_{p \in s}^{\;}\; {\langle{\prod\limits_{i \in p}^{\;}\; {I\left( {{\overset{\rightarrow}{p}}_{i},{t - \tau_{i}}} \right)}}\rangle}_{t}}}}},$

where

. . .

_(t) stands for averaging over the time t, s runs over all partitions ofthe set S={1, 2, . . . , n}, p enumerates the q_(s) subsets or parts ofpartition s and I({right arrow over (p)},t) is the intensitydistribution measured over time on a detector pixel {right arrow over(p)}.

FIG. 2 illustrates the different steps for computing higher-ordercumulants from the acquired images 41. The data 51 contained in thememory buffer 40, corresponds to the captured light intensities of thepoint-like emitters. The intensity time traces of pixels 53, 54, 55 areindicated in 56, 57, 58. These representative pixel traces 52 are theinput elements 61 for the cumulant-processing unit 62, calculating then-th order cumulant 63 according to [0026].

As a consequence of additivity, the cumulant of a sum of independentrandom variables (e.g. independently blinking point-like emitters)corresponds to the sum of the cumulants of each individual randomvariable. The intensity distribution I({right arrow over (p)},t) of asample composed of N independently fluctuating point-like emitters canbe written as

${I\left( {\overset{\rightarrow}{p},t} \right)} = {{\sum\limits_{k = 1}^{N}{A_{k}{U\left( {\overset{\rightarrow}{p} - \overset{\rightarrow}{r_{k}}} \right)}{s_{k}(t)}}} + {b\left( \overset{\rightarrow}{p} \right)}}$

where A_(k),{right arrow over (r)}_(k) and s_(k) denote the emitter'sbrightness, position and normalized temporal fluctuation signal, U(r) isthe system's PSF and b represents a temporally constant background term.Taking the n-th order cumulant leads to

$\begin{matrix}{{\kappa_{n}\left\{ {I\left( {{\overset{\rightarrow}{p}}_{i},t} \right)} \right\}} = {{\sum\limits_{k = 1}^{N}{\kappa_{n}\left\{ {A_{k}{U\left( {\overset{\rightarrow}{p} - \overset{\rightarrow}{r_{k}}} \right)}{s_{k}(t)}} \right\}}} + {\kappa_{n}\left\{ {b\left( \overset{\rightarrow}{p} \right)} \right\}}}} \\{= {\sum\limits_{k = 1}^{N}\left\{ {{A_{k}^{n}{U^{n}\left( {\overset{\rightarrow}{p} - \overset{\rightarrow}{r_{k}}} \right)}\omega_{n,k}} + \left\{ \begin{matrix}{b\left( \overset{\rightarrow}{p} \right)} & {n = 1} \\0 & {n > 1}\end{matrix} \right.} \right.}}\end{matrix}$

with ω_(n,k)=κ_(n){s_(k)(t)}_(t) a weighting factor depending on thecharacteristic blinking properties of the emitter k. If we approximateU(r) by a Gaussian function, U^(n)(r) yields again a Gaussian functionwith a √{square root over (n)}-fold reduced size in all dimensionsleading to a in √{square root over (n)}-fold improved resolution.

Apart from the super-resolved structural information revealed byhigher-order cumulants, the weighting factorsω_(n,k)=κ_(n){s_(k)(t)}_(t) also contain exploitable informationconcerning the photo-physics of each emitter, which can be extracted byconsidering multiple cumulant orders. In the simplest case, the emitterfluctuates between two states (corresponding to a Bernoullidistribution), a bright state S_(on) and a dark state S_(off). Therelative amount of time it stays in the state S_(on) and S_(off),respectively, can be defined as

${\rho_{on} = \frac{\tau_{on}}{\tau_{on} + \tau_{off}}},\begin{matrix}{\rho_{off} = \frac{\tau_{off}}{\tau_{on} + \tau_{off}}} \\{= {1 - \rho_{m}}}\end{matrix},$

where τ_(on) and τ_(off) off are the lifetimes of the states S_(on) andS_(off). We define the normalized temporal fluctuation signal s_(k)(t)to be 1 when the emitter is in the state S_(on) and ε∈[0,1) when it isin the state S_(off). The weighting factors ω_(n,k) of the first fourorders become then

ω_(1; k) = (1 − ɛ_(k))ρ_(on, k)ω_(2; k) = (1 − ɛ_(k))²ρ_(on, k)(1 − ρ_(on, k))ω_(3; k) = (1 − ɛ_(k))³ρ_(on, k)(1 − ρ_(on, k))(1 − 2ρ_(on, k))ω_(4; k) = (1 − ɛ_(k))⁴ρ_(on, k)(1 − ρ_(on, k))(1 − 6ρ_(on, k) + 6ρ_(on, k)²)⋮ ω_(n; k) = (1 − ɛ_(k))^(n)f_(n)(ρ_(on, k)),

with

${f_{n}\left( \rho_{{on},k} \right)} = {{\rho_{{on},k}\left( {1 - \rho_{{on},k}} \right)}\frac{\partial f_{n - 1}}{\partial\rho_{{on},k}}}$

the n-th order cumulant of a Bernoulli distribution with probabilityρ_(on,k). Since parameters, such as the molecular state lifetimes andthe molecular brightness depend on the local environment, the oxygenconcentration influences the dark-state lifetime of organic fluorophoresfor instance, we assume region-dependent but locally constant on-timeratios and amplitudes. The overall cumulants may then be approximated by

${\kappa_{1}\left( \overset{\rightarrow}{p} \right)} = {{{{\hat{A}\left( \overset{\rightarrow}{p} \right)}{\rho_{on}\left( \overset{\rightarrow}{p} \right)}{\sum\limits_{k = 1}^{N}{U\left( {\overset{\rightarrow}{p} - {\overset{\rightarrow}{r}}_{k}} \right)}}} + {b\left( \overset{\rightarrow}{p} \right)}} \approx {{{\hat{A}\left( \overset{\rightarrow}{p} \right)}{\hat{N}\left( \overset{\rightarrow}{p} \right)}E\left\{ {U\left( \overset{\rightarrow}{p} \right)} \right\} {\rho_{on}\left( \overset{\rightarrow}{p} \right)}} + {b\left( \overset{\rightarrow}{p} \right)}}}$${\kappa_{2}\left( \overset{\rightarrow}{p} \right)} \approx {{\hat{N}\left( \overset{\rightarrow}{p} \right)}{{\hat{A}}^{2}\left( \overset{\rightarrow}{p} \right)}E\left\{ {U^{2}\left( \overset{\rightarrow}{p} \right)} \right\} {\rho_{on}\left( \overset{\rightarrow}{p} \right)}\left( {1 - {\rho_{on}\left( \overset{\rightarrow}{p} \right)}} \right)}$${\kappa_{3}\left( \overset{\rightarrow}{p} \right)} \approx {{\hat{N}\left( \overset{\rightarrow}{p} \right)}{{\hat{A}}^{3}\left( \overset{\rightarrow}{p} \right)}E\left\{ {U^{3}\left( \overset{\rightarrow}{p} \right)} \right\} {\rho_{on}\left( \overset{\rightarrow}{p} \right)}\left( {1 - {\rho_{on}\left( \overset{\rightarrow}{p} \right)}} \right)\left( {1 - {2{\rho_{on}\left( \overset{\rightarrow}{p} \right)}}} \right)}$${\kappa_{4}\left( \overset{\rightarrow}{p} \right)} \approx {{\hat{N}\left( \overset{\rightarrow}{p} \right)}{{\hat{A}}^{4}\left( \overset{\rightarrow}{p} \right)}E\left\{ {U^{4}\left( \overset{\rightarrow}{p} \right)} \right\} {\rho_{on}\left( \overset{\rightarrow}{p} \right)}\left( {1 - {\rho_{on}\left( \overset{\rightarrow}{p} \right)}} \right)\left( {1 - {6{\rho_{on}\left( \overset{\rightarrow}{p} \right)}} + {6{\rho_{on}^{2}\left( \overset{\rightarrow}{p} \right)}}} \right)}$⋮${{\kappa_{n}\left( \overset{\rightarrow}{p} \right)} \approx {{\hat{N}\left( \overset{\rightarrow}{p} \right)}{{\hat{A}}^{n}\left( \overset{\rightarrow}{p} \right)}E\left\{ {U^{n}\left( \overset{\rightarrow}{p} \right)} \right\} {f_{n}\left( {\rho_{on};\overset{\rightarrow}{p}} \right)}}},$

where E{ . . . } is the expectation operator. For a Gaussian PSF, then-th order moment can be written as

${{E\left\{ {U^{n}\left( \overset{\rightarrow}{p} \right)} \right\}}\overset{\sim}{=}\frac{c\left( {\sigma_{xy},\sigma_{z}} \right)}{n^{3/2}}},$

with c(σ_(xy),σ_(z)) a constant depending on the spatial extent of thePSF. Finally, we can write

${\kappa_{n}\left( \overset{\rightarrow}{p} \right)} \approx {\frac{c}{n^{3/2}}{\hat{N}\left( \overset{\rightarrow}{p} \right)}{{\hat{A}}^{n}\left( \overset{\rightarrow}{p} \right)}{f_{n}\left( {\rho_{on};\overset{\rightarrow}{p}} \right)}}$

which then enables the pixel-wise estimation of the parameters{circumflex over (N)}({right arrow over (p)}), Â({right arrow over (p)})and ρ_(on)({right arrow over (p)}) by considering three or more cumulantorders.

To estimate the parameters of a two-state system assuming a GaussianPSF, cumulant orders two to four can be used to build the ratios

$\begin{matrix}{{K_{1}\left( \overset{\rightarrow}{p} \right)} = {\frac{3^{3/2}\kappa_{3}}{2^{3/2}\kappa_{2}}\left( \overset{\rightarrow}{p} \right)}} \\{= {{\hat{A}\left( \overset{\rightarrow}{p} \right)}\left\lbrack {1 - {2{\rho_{1}\left( \overset{\rightarrow}{p} \right)}}} \right\rbrack}}\end{matrix}$ $\begin{matrix}{{K_{2}\left( \overset{\rightarrow}{p} \right)} = {\frac{4^{3/2}\kappa_{4}}{2^{3/2}\kappa_{2}}\left( \overset{\rightarrow}{p} \right)}} \\{= {{{\hat{A}}^{2}\left( \overset{\rightarrow}{p} \right)}\left\lbrack {1 - {6{\rho_{1}\left( \overset{\rightarrow}{p} \right)}} + {6{\rho_{1}^{2}\left( \overset{\rightarrow}{p} \right)}}} \right\rbrack}}\end{matrix}$

and to solve for the amplitude

Â({right arrow over (p)})=√{square root over (3K ₁ ²({right arrow over(p)})−2K ₂({right arrow over (p)}))},

${\rho_{on}\left( \overset{->}{p} \right)} = {\frac{1}{2} - \frac{K_{1}\left( \overset{->}{p} \right)}{2\; {\hat{A}\left( \overset{->}{p} \right)}}}$

and the number of particles

${N\left( \overset{->}{p} \right)} = {\frac{\kappa_{2}\left( \overset{->}{p} \right)}{{{\hat{A}}^{2}\left( \overset{->}{p} \right)}{{\rho_{on}\left( \overset{->}{p} \right)}\left\lbrack {1 - {\rho_{on}\left( \overset{->}{p} \right)}} \right\rbrack}}.}$

The spatial resolution of the estimation is given by the lowest ordercumulant, i.e. the second order in the outlined example. However, thepresented solution is not unique. In principle, any three distinctcumulant orders could have been used to provide a solution by solvingthe equation system or using a fitting procedure. Furthermore, themethod is not limited to a two-state system; it can be extended to amulti-state system (for example a decreased emission due to an energytransfer to an acceptor approaching the emitter), as long as theirdifferences can be detected with the imaging setup.

If in addition the cumulants are computed for different sets of timelags and the acquisition rate oversamples the blinking rate, it is alsopossible to extract absolute estimates on the characteristic lifetimesof the different states. In a two-state system, using the second ordercumulant for example, which is equivalent to a centred second ordercorrelation, it is sufficient to measure the temporal extent of thecorrelation curve before it approaches zero to get an estimate on theblinking period. The lifetimes of the on- and off-state can becalculated easily from the estimated on-time ratio and the blinkingperiod.

The flowchart 70 in FIG. 3 summarizes the different steps involved forobtaining the parameter maps {circumflex over (N)}({right arrow over(p)}), Â({right arrow over (p)}), ρ_(on)({right arrow over (p)}),τ_(on)({right arrow over (p)}) and τ_(off)({right arrow over (p)}) asdescribed and indicated by the formulas above. For displaying theparameter maps 74, one can for example use a colour coding of theparameter values and overlay a cumulant or balanced cumulant (asdescribed in the following paragraphs) image of any order as an alpha ortransparency map, in order to suppress arbitrary parameter estimationsin the background of the sample.

Embodiment 1 Balanced Cumulants

Computing higher-order cumulants for structural super-resolutionmicroscopy amplifies heterogeneities in molecular brightness andblinking. As described in paragraphs [0029] and [0030], the underlyingmolecular photo-physics can be extracted by combining the information ofseveral cumulant orders, which allows correcting the resulting amplifiedheterogeneities and retrieving hidden information.

As shown in paragraph [0029], the n-th order cumulant of independentlyblinking emitters may be approximated by

$\begin{matrix}{{\kappa_{n}\left( \overset{->}{p} \right)} \approx {{{\hat{A}}^{n}\left( \overset{->}{p} \right)}{f_{n}\left( {\rho_{on};\overset{->}{p}} \right)}{\sum\limits_{k = 1}^{N}{U^{n}\left( {\overset{->}{p} - {\overset{->}{r}}_{k}} \right)}}}} \\{\approx {{{\hat{A}}^{n}\left( \overset{->}{p} \right)}{f_{n}\left( {\rho_{on};\overset{->}{p}} \right)}{\sum\limits_{k = 1}^{N}{{\delta\left( {\overset{->}{p} - {\overset{->}{r}}_{k}} \right)}*{U^{n}\left( \overset{->}{p} \right)}}}}}\end{matrix}$

FIG. 4 shows a flowchart for computing balanced cumulants (80). Afterdata acquisition 81 and cumulant computation 82 as described inparagraph [0026], κ_(n)({right arrow over (p)}) is spatially deconvolvedwith any suitable algorithm 83, for example by using Wiener filtering:

${{{\overset{\Cup}{\kappa}}_{n}\left( \overset{->}{p} \right)} = {F^{- 1}\left\{ {F{\left\{ {\kappa_{n}\left( \overset{->}{p} \right)} \right\} \cdot \frac{\left( {F\left\{ {U^{n}\left( \overset{->}{p} \right)} \right\}} \right)^{*}}{{\left( {F\left\{ {U^{n}\left( \overset{->}{p} \right)} \right\}} \right)^{*}F\left\{ {U^{n}\left( \overset{->}{p} \right)} \right\}} + \alpha}}} \right\}}},{\alpha 1},$

where F{ . . . } and F⁻¹{ . . . } denote the forward and inverse Fouriertransforms, and α is a regularization constant to avoid a division byzero. As a result, we would obtain ideally

${{\overset{\Cup}{\kappa}}_{n}\left( \overset{->}{p} \right)} \approx {{{\hat{A}}^{n}\left( \overset{->}{p} \right)}{f_{n}\left( {\rho_{on};\overset{->}{p}} \right)}{\sum\limits_{k = 1}^{N}{{\delta\left( {\overset{->}{p} - {\overset{->}{r}}_{k}} \right)}.}}}$

This intermediate deconvolution step is needed to correct for theheterogeneities without compromising on spatial resolution.

In parallel to the deconvolution, a combination of different cumulantorders is used to estimate the on-time ratio ρ_(on)({right arrow over(p)}) 84 as described in paragraphs [0029] and [0030] and to calculatef_(n)(ρ_(on);{right arrow over (p)}). Using the deconvolved cumulant{hacek over (κ)}_(n)({right arrow over (p)}) and the polynomialf_(n)(ρ_(on);{right arrow over (p)}), we can calculate brightnessbalanced cumulants (BC) with a linear response to the molecularbrightness or photon balanced cumulants (BC^(P)) with a linear responseto the amount of photons collected 85, according to

${{{BC}_{n}\left( \overset{->}{p} \right)} = {\sqrt[n]{\frac{{\overset{\Cup}{\kappa}}_{n}\left( \overset{->}{p} \right)}{{sgn}\left\{ {f_{n}\left( {\rho_{on};\overset{->}{p}} \right)} \right\} \left( {{{f_{n}\left( {\rho_{on};\overset{->}{p}} \right)}} + \beta} \right)}}*{U^{n}\left( \overset{->}{p} \right)}}},{\beta 1},$

respectively

${{{BC}_{n}^{p}\left( \overset{->}{p} \right)} = {\sqrt[n]{\frac{{\overset{\Cup}{\kappa}}_{n}\left( \overset{->}{p} \right)}{{sgn}\left\{ {{f_{n}\left( {\rho_{on};\overset{->}{p}} \right)}/{\rho_{on}\left( \overset{->}{p} \right)}} \right\} \left( {{{{f_{n}\left( {\rho_{on};\overset{->}{p}} \right)}/{\rho_{on}\left( \overset{->}{p} \right)}}} + \beta} \right)}}*{U^{n}\left( \overset{->}{p} \right)}}},{\beta 1.}$

The result of the division of the deconvolved cumulant {hacek over(κ)}_(n)({right arrow over (p)}) by the polynomial f_(n)(ρ_(on);{rightarrow over (p)}), respectively f_(n)(ρ_(on);{right arrow over(p)})/ρ_(on)({right arrow over (p)}) should be positive everywhere.Negative values arise from artefacts and hence can be truncated. Itshould be noted, that this division might amplify structural artefactsin regions of low signal-to-noise ratios (i.e. where f_(n)(ρ_(on);{rightarrow over (p)}) is close to 0). However, since the roots off_(n)(ρ_(on);{right arrow over (p)}) are distinct for every n, theseregions can be easily replaced with the result from the balancedcumulant order n−1 or n+1, which then results in a better overall imagequality. The reconvolution with the PSF raised to the power of n afterthe linearization is optional, but recommended in order to minimize theamount of introduced image artefacts.

The right part (90) of FIG. 4 illustrates the effect of heterogeneousamplitude and/or on-time ratio distributions on the resulting cumulantorders 1 to 4 (92) with a selective amplification of some of theemitters and how the balanced cumulants 93 can retrieve the attenuatedemitters. The brightness-balanced cumulants can be interpreted as thesum of the individual molecular amplitudes convolved by the PSF raisedto the power of n

$\begin{matrix}{{{BC}_{n}\left( \overset{->}{p} \right)} \approx {\sum\limits_{k = 1}^{N}{A_{k}{\delta\left( {\overset{->}{p} - {\overset{->}{r}}_{k}} \right)}*{U^{n}\left( \overset{->}{p} \right)}}}} \\{{\approx {\sum\limits_{k = 1}^{N}{A_{k}{U^{n}\left( {\overset{->}{p} - {\overset{->}{r}}_{k}} \right)}}}},}\end{matrix}$

whereas the photon balanced cumulants additionally involve the on-timeratio

${{BC}_{n}^{p}\left( \overset{->}{p} \right)} \approx {\sum\limits_{k = 1}^{N}{A_{k}\rho_{{on},k}{{U^{n}\left( {\overset{->}{p} - {\overset{->}{r}}_{k}} \right)}.}}}$

Since the cumulant equivalent optical transfer function (cOTF)corresponds to an n-fold convolution of the imaging system's OTF, thesupport of the cOTF, respectively the cut-off spatial frequency, scaleslinearly with the order n. By applying a simple reweighting scheme inthe Fourier domain of the n-th order cumulant, a final resolutionimprovement that scales almost linearly with n can be achieved (seeDertinger et al., Opt. Express 2010):

${{\kappa_{n;{FRW}}\left( \overset{->}{p} \right)} = {F^{- 1}\left\{ \frac{F\left\{ {\kappa_{n}\left( \overset{->}{p} \right)} \right\} F\left\{ {U\left( {n\overset{->}{p}} \right)} \right\}}{{F\left\{ {U^{n}\left( \overset{->}{p} \right)} \right\}} + \gamma} \right\}}},{\gamma 1.}$

Accordingly for balanced cumulants, instead of convolving withU^(n)({right arrow over (p)}) (paragraph [0037]), it is also possible toconvolve with the n-times size-reduced PSF U(n{right arrow over (p)}),without significantly pronouncing non-physical artefacts.

FIG. 5 shows a 1D example comparing unbalanced and balanced cumulants oftwo emitters located at x₁ and x₂ with amplitudes 1 and 0.6 and on-timeratios 0.5 and 0.25. The left part 100 illustrates the mean intensitydistribution observed on a detector 101, which corresponds to the sum ofthe time-averaged responses of each emitter 102,103 being the emitters'amplitudes times the respective on-time ratios and the system's PSF. Theright part 110 illustrates the results of the balanced and unbalancedcumulants. The curve 111 corresponds to the first order cumulant, or themean image, curves 112 and 113 represent the unbalanced cumulant oforder 4 without, respectively with Fourier reweighting and 114, 115 showthe photon, respectively brightness balanced cumulants (BC^(p), BC),which reveal the presence of emitter 2.

Embodiment 2 Cumulant Microscopy Combined with Single MoleculeLocalization

The estimation of the on-time ratio and the labelling density is crucialfor single molecule localization with a minor percentage of falselocalizations. Cumulant microscopy can provide an estimate on thespatial distribution of these parameters (paragraphs [0029] and [0030]),which in turn can be used to perform single molecule localization inregions with suitable on-time ratios and labelling densities, whereas inthe other regions the cumulant image is used for providing more details.

Embodiment 3 Microenvironment Sensitive Imaging

As mentioned above, fluorescence blinking is highly sensitive to thechemical microenvironment. For example, if the observed blinking is dueto cycling between the singlet states (bright state) and the excitedtriplet state of a fluorophore or any other state mediated by thetriplet state (dark state), the on-time ratio is highly influenced bythe concentration of triplet state quenchers, like for example oxygen.Oxygen in its normal form is in a triplet state and upon collision witha fluorophore being in its excited triplet state, an energy transfer mayhappen, transforming the fluorophore back to its fundamental groundstate and oxygen to an excited and highly reactive singlet state. Thepresence of oxygen thus reduces the dark state lifetime and accordinglyincreases the on-time ratio, which therefore could be used as an oxygensensor.

If reducing or oxidizing agents are present, there exist alternativerelaxation pathways from excited states of fluorophores that mayinfluence the blinking behaviour. For example, cells are highly complexsystems with many different local environments and organelles. Aspatially super-resolved statistical analysis of the molecular blinkingprovides additional information, which might be used to deduce some ofthe properties (chemical, temperature, pressure, local pH, etc.) of thesurrounding microenvironments and thus help for a better understandingof biological processes at a subcellular level.

Embodiment 4 Functional Super-Resolution Microscopy Exploiting TripletBlinking

Ideal probes for cumulant microscopy are bright and provide manyblinking cycles. Nonetheless, the required minimum number of detectedphotons in a bright state can be much lower than for localization-basedtechniques, in the order of tens of photons per molecule and on-statelifetime (see Geissbuehler et al., Biomed. Opt. Express 2011).Therefore, the fast stochastic blinking of fluorophores induced bycycling between the bright singlet states and the dark excited tripletstate should already yield sufficient photons per cycle to performcumulant microscopy.

The triplet state is common to almost all fluorophores, has a typicallifetime of about 1000 times the corresponding singlet lifetime andresults in a non-radiative relaxation or weak phosphorescence. However,the triplet state excitation and relaxation is usually too fast to becaptured by a state-of-the-art microscopy camera and the fluctuationsare averaged out. In order to overcome the speed limit of the camera, itis necessary to apply a modulated excitation with pulse durations of theorder of the triplet lifetime and synchronize it with the detection.Even so, the resulting dead time between the pulses is much higher thanthe triplet lifetime, such that most molecules return to the singletground state and are re-excited with the next pump pulse without passingto the triplet state. As a result, the observed fluctuations would bevery weak and barely detectable. To overcome this issue, a specialexcitation modulation scheme 121 with synchronized detection 122, asillustrated in FIG. 6, is applied to populate the triplet state 124 andprobe the proportion of molecules remaining in the singlet state with aprobe pulse 125 of the order of the triplet lifetime. The population ofthe triplet state 124 is done during the readout 127 of the camera witha pre-pulse 123 prior to the exposure 126. The camera needs to have afast charge clearing 128 (compared to the triplet lifetime) just beforethe exposure 126. Due to the lack of a pre-pulse, the first frame 129shows only a weak triplet population and should be omitted from thefinal image sequence.

An example wide-field implementation of this technique is shown in FIG.7. An acousto- or electro-optical modulator 134 is used to generate thepulse sequence in the excitation beam 135. A function generator 132controls the modulator and triggers the camera 141 according to themodulation scheme illustrated in FIG. 6. The excitation beam 135 isfocused in the back aperture of the objective 136 and is directed onto afluorescently labelled sample 137. Some of the emitted fluorescence 140is collected by the objective 136, separated and filtered from theexcitation by a filter cube 138 and focused onto the array detector ofthe camera 141. The camera is linked to a computer 131, which is alsoused for data processing.

The small number of photons collected during the short probe pulse isinsufficient to perform localization microscopy but it should besufficient for cumulant microscopy.

An alternative implementation to capture the triplet state fluctuationsis the use of a time-gated camera combined with either a synchronizedmodulated excitation or a continuous illumination.

It is also possible to exploit the triplet blinking in a confocaldetection scheme, where for every scanning point a time trace isrecorded. State-of-the-art single point photo-detectors (e.g. avalanchephotodiodes) provide the necessary speed to capture the triplet blinkingdirectly, which waives the need for a modulated excitation scheme.

Embodiment 5 Excitation-Induced Fluctuations

In order to expand the range of suitable probes, stochastic fluctuationsmay also be induced via a fluctuating excitation. Hereto, a varyingspeckle illumination shall be generated (e.g. by a diffuser platemounted on a motorized rotation stage), which imposes stochasticintensity fluctuations in the specimen. Because the size of speckles isdiffraction-limited, the fluctuations of closely spaced emitters arecorrelated and hence the resolution is also diffraction-limited.However, if we take advantage of non-linear effects, e.g. exploiting anyreversibly saturable optical transition, either the bright or the darkregions can become smaller than a diffraction-limited spot and hence thespatial extent of correlated excitation fluctuations shrinksaccordingly.

Embodiment 6 Continuous Cumulation with Hardware Support

In principle, the calculation of cumulants requires access to the entiretime series of recorded images, which means that the cumulants can onlybe evaluated a posteriori—once the recording is complete. Thisembodiment describes a method for calculating cumulants by processingthe captured images in small time intervals, which allows updating anddisplaying the cumulants during the measurement. The result of thiscontinuous (live) processing shall be identical to the evaluation aposteriori.

The cumulant κ_(n) of order n is obtained as a linear combination ofproducts formed from partial products. These partial products areestimated temporal averages

${{\overset{\_}{P}}_{s} = {\langle{\prod\limits_{i \in s}{I\left( {{\overset{->}{p}}_{i},t} \right)}}\rangle}_{t}},$

where I({right arrow over (p)}_(i),t) is the intensity measured at timet on pixel {right arrow over (p)}_(i) and s is a part of partition S.For evaluating the linear combination, the partial products P_(s) haveto be known, which prohibits a continuous accumulation in the cumulantκ_(n) itself. A continuous accumulation can only be performed for thepartial products P_(s) required for κ_(n). The linear combination has tobe re-evaluated each time an update of κ_(n) is requested.

The method is implemented as follows (the flowchart in FIG. 8 lists themain steps):

(1) the captured images from the camera 151 are transferred to andstored in a memory buffer 152.(2) The buffered images are processed 153 from time to time by updatingthe partial products P_(s) in which the aggregate values of all capturedimages are accumulated 154.(3) Each time step 2 completes, the cumulant κ_(n), 155 is re-evaluatedbased on P_(s) =P_(s)/κ_(n) where K is the number of yet accumulatedimages.(4) An update of κ_(n) or of derived parameters is displayed 156.(5) A control task manages and synchronizes the actions of the hard- andsoftware implied in steps 1 to 4.(6) The user interacts with this control task by a user interface.

Step 2 implies many but simple multiplications and additions of integervalues. These calculations have to be performed timely in order toprocess the images at least as fast as the camera captures them. Apossible embodiment outsources this processing to a dedicated hardwaremodule, an FPGA board or a powerful graphics processor (GPU) 153 forinstance. This very same module may be used to receive the images fromthe camera directly (step 1), i.e. by bypassing the shared resources ofthe computer. This is particularly interesting for calculating higherorder cumulants, as the required memory throughput and the requiredprocessing speed quickly increase.

Embodiment 7 Widefield Multi-Focal Plane Acquisition and 3DCross-Cumulation

As described in PCT/US2010/037099, cross-cumulants can be used toincrease the pixel grid density, so that the final resolution is notlimited by the effective pixel size. Cross-cumulation can be performedin any spatial direction, including the axial dimension, resulting in upto n³ times the original number of pixels. To maximize speed andfield-of-view it makes sense to over-sample the system's PSF just asmuch as needed to satisfy Shannon's sampling theorem (Shannon, C. E.Proc. I.R.B., vol. 37, pp. 10-21, 1949) and to ensure a correlatedsignal for individual emitters with the specific pixel combinations usedin the cross-cumulants (depending on the signal-to-noise ratio). Ingeneral, the more pixels are acquired in parallel, the faster is theoverall image acquisition. It is thus advantageous to use a widefieldimaging system with a high pixel-count camera sensitive and fast enoughto detect the emitters' fluctuations.

For widefield 3D cumulant microscopy, instead of acquiring the axialsections sequentially, it is possible to acquire multiple depth or focusplanes in parallel using a special detection scheme. The benefit of aparallel depth acquisition is a better exploitation of the availablephoton budget (especially if the emitters suffer from bleaching) whenilluminating the whole sample depth. Furthermore, the resulting contrastof the 3D cross-cumulants as compared to sequentially applied 2Dcross-cumulants is expected to be more homogeneous along the opticalaxis, due to the fact that the fluctuations are stochastic and thus thecumulant response of a single emitter might change with the time and thesequentially acquired depth sections. The eventually imbalanced cumulantcontrast might be problematic for a 3D Fourier reweighting (Dertinger etal., Opt. Express 2010) or a cumulant balancing as described inEmbodiment 1.

FIG. 9 describes a possible and arbitrarily expandable detection schemefor a parallel acquisition of multiple focal planes or focal channels.It consists of a widefield detection system (161 would be in theinfinity path of the microscope) that provides the access to anintermediate image plane via some relay optics 162 for introducing anadjustable field stop 163, m diagonally arranged 50/50 beamsplitters 165after the tube lens 164 and 2m-2 adjustable mirrors (166 and 167) withtwo angular degrees of freedom and half of them 167 providing anadditional translational (along the optical axis) degree of freedom, aswell as 2 cameras (168 and 169) with one being displaceable along theaxis 168. By displacing the mirrors and one camera along the opticalaxis, it is possible to set up 2^(m) distinct optical path lengths withrespect to the tube lens and thus probe 2^(m) distinct focal planes. Theangular degrees of freedom of the mirrors 166 and 167 are used toarrange the focal planes next to each other such that they fit on thecamera sensors 170. The distance between the planes should not exceedhalf the axial resolution of the imaging system to comply with Shannon'ssampling theorem. The field stop 163 ideally has a rectangular,size-adjustable form and is used to avoid cross talk among the channels.

If the emitters blink fast with respect to the camera frame-rate, itmight be necessary to use a zero time lag for the calculation ofcumulants to ensure a signal from single emitters. Cross-cumulants thenpresent significant advantages over auto-cumulants concerning theelimination of noise. It is thus advantageous to use only pixelcombinations without repetitions (see Geissbuehler et al., Biomed. Opt.Express 2011). FIG. 10 shows possible pixel combinations for computing a3D fourth-order cross-cumulant with a 64-fold increase in pixel count.The acquired intensity time traces of pixels from two distinct focalplanes or channels (181 and 182, denoted by a single letter withrespectively without an apostrophe to distinguish between the two focalplanes) are combined in cross-cumulants to generate inter-pixels 183 inbetween the original pixel matrix.

Instead of a combination of multiple beamsplitters and mirrors togenerate multiple focal planes as described in [0058], it is alsopossible to achieve a grid arrangement of multiple focal planes on asingle camera using a specifically designed phase or amplitude maskplaced in a Fourier plane conjugated to the back-aperture of theobjective (i.e. before the tube lens 164).

Embodiment 8 Multi-Colour Cumulant Microscopy Using SpectralCross-Cumulation

In the following paragraphs, we provide a generalized concept forspectrally unmixing multiple emitter species using cumulants.

If the detection arm of the imaging setup contains at least one spectralsplitter (e.g. dichroic mirror), which divides the detection beam intotwo or more spectrally distinct beams that are focused onto two or moredistinct detectors or detection areas, cumulant microscopy can also beapplied to multi-colour specimens containing multiple, spectrallydistinct emitter species.

In the simplest case, a single spectral beam splitter is used togenerate two detection channels (C₁ and C₂) with specific spectralresponse curves. FIG. 11 shows an example with a single spectral beamsplitter 193 and two detector channels C₁ [194] and C₂ [195] resultingin the spectral response curves s₁ and s₂ [196]. Let m be the number ofdistinct emitter species with distinct emission spectra (197 in FIG. 11)that fluctuate stochastically and independently. For the distinction ofseveral emitter species using spectral cross-cumulants, the emissionspectra should have an overlap with both spectral response curves of thedetection channels. Due to the additivity, the cumulant of multipleindependent species corresponds to the sum of the cumulants of eachindividual species:

${{\kappa_{n}\left\{ {\sum\limits_{i = 1}^{m}{I_{i}\left( {\overset{->}{p},t} \right)}} \right\}_{t}} = {\sum\limits_{i = 1}^{m}{\kappa_{n}\left\{ {I_{i}\left( {\overset{->}{p},t} \right)} \right\}_{t}}}},$

with I_(i)({right arrow over (p)},t) being the intensity distribution ofemitter species i measured on pixel {right arrow over (p)} over time t.

A calibration is needed before starting multi-colour imagingexperiments. To this end, the relative, ratio-metric intensity responseof the two channels (R_(i)=I_(C) ₂ _(,i)/I_(C) ₁ _(,i)) is measured foreach single emitter species under similar conditions as the envisagedexperiments. In the example of FIG. 11, estimating from 196 and 197, theratios would correspond to R₁=0.6 and R₂=7. Next, we compute spectralcross-cumulants of order n, which involve u pixels from channel C₁ and(n−u) pixels from channel C₂. The involved pixels have to probespatially overlapping detection volumes in the object space. The resultof this spectral cross-cumulation can be interpreted as

${{\kappa_{n;{C_{1}^{u}C_{2}^{n - u}}}\left( \overset{->}{p} \right)} = {\sum\limits_{i = 1}^{m}{R_{i}^{n - u}\kappa_{n}\left\{ {I_{i;C_{1}}\left( {\overset{->}{p},t} \right)} \right\}_{t}}}},$

where I_(i;C) ₁ ({right arrow over (p)},t) stands for the intensitydistribution of the isolated species i measured on detector channel C₁.

To extract the unknown cumulants of the individual emitter speciesκ_(n){I_(i;C) ₁ ({right arrow over (p)},t)}_(t) it is sufficient tocompute m spectral cross-cumulants with distinct combinations of pixelsto generate a linear equation system, which is then solved for the munknown cumulants. For example, the following equation system

${\begin{bmatrix}R_{1}^{n - 1} & R_{2}^{n - 1} & \ldots & R_{m}^{n - 1} \\R_{1}^{n - 2} & R_{2}^{n - 2} & \ldots & R_{m}^{n - 2} \\\vdots & \vdots & \vdots & \vdots \\R_{1}^{n - m} & R_{2}^{n - m} & \ldots & R_{m}^{n - m}\end{bmatrix}\begin{bmatrix}{\kappa_{n}\left\{ {I_{1;C_{1}}\left( {\overset{->}{p},t} \right)} \right\}_{t}} \\{\kappa_{n}\left\{ {I_{2;C_{1}}\left( {\overset{->}{p},t} \right)} \right\}_{t}} \\\vdots \\{\kappa_{n}\left\{ {I_{m;C_{1}}\left( {\overset{->}{p},t} \right)} \right\}_{t}}\end{bmatrix}} = \begin{bmatrix}{\kappa_{n;{C_{1}^{1}C_{2}^{n - 1}}}\left( \overset{->}{p} \right)} \\{\kappa_{n;{C_{1}^{2}C_{2}^{n - 2}}}\left( \overset{->}{p} \right)} \\\vdots \\{\kappa_{n;{C_{1}^{m}C_{2}^{n - m}}}\left( \overset{->}{p} \right)}\end{bmatrix}$

allows to obtain the desired spectral unmixing by matrix inversion:

$\begin{bmatrix}{\kappa_{n}\left\{ {I_{1;C_{1}}\left( {\overset{->}{p},t} \right)} \right\}_{t}} \\{\kappa_{n}\left\{ {I_{2;C_{1}}\left( {\overset{->}{p},t} \right)} \right\}_{t}} \\\vdots \\{\kappa_{n}\left\{ {I_{m;C_{1}}\left( {\overset{->}{p},t} \right)} \right\}_{t}}\end{bmatrix} = {\begin{bmatrix}R_{1}^{n - 1} & R_{2}^{n - 1} & \ldots & R_{m}^{n - 1} \\R_{1}^{n - 2} & R_{2}^{n - 2} & \ldots & R_{m}^{n - 2} \\\vdots & \vdots & \vdots & \vdots \\R_{1}^{n - m} & R_{2}^{n - m} & \ldots & R_{m}^{n - m}\end{bmatrix}^{- 1}\begin{bmatrix}{\kappa_{n;{C_{1}^{1}C_{2}^{n - 1}}}\left( \overset{->}{p} \right)} \\{\kappa_{n;{C_{1}^{2}C_{2}^{n - 2}}}\left( \overset{->}{p} \right)} \\\vdots \\{\kappa_{n;{C_{1}^{m}C_{2}^{n - m}}}\left( \overset{->}{p} \right)}\end{bmatrix}}$

In the above development, we assumed that all pixels probe the sameposition in the object space. However, the concept can easily be adaptedfor spatially distinct pixel positions by introducing a distance factorthat corrects for the decrease in spatial correlation for a given set ofpixel positions (in analogy to Dertinger et al., Opt Express 2010).

Obviously, if the emitter species can already be spectrally separated bythe detection channels themselves without significant cross talk, theunmixing is provided without the need for spectral cross-cumulation.

1. Method for imaging and analysing an object labelled withstochastically and independently blinking point-like emitters, saidmethod comprising the following steps: Acquiring a time series of imagesfrom blinking point-like emitters, Calculating higher-order cumulantsfrom said acquired images, Determining at least the parameter maps formolecular state lifetimes, amplitude and concentration of said emittersby establishing a multi-state blinking model, expressing severalcumulant orders as a function of the parameters involved and solving theresulting equations for the parameters, Obtaining a balanced cumulant byspatially deconvolving the cumulant of order n, by taking then the n-throot and by compensating for the temporal weighting factors using thepreviously determined parameter maps, Displaying said parameter maps andbalanced cumulants in a way as to obtain information about thestructural and/or functional features of the object reported by saidemitters.
 2. Method according to claim 1 comprising a step wherein atleast one of the following spatially variable but temporally constanttwo-state blinking parameter maps is obtained: N(p), A(p), ρ_(oη)(ρ),τ_(oη)(ρ) or off {P) wherein N(p) is the number of particles, A(p) isthe amplitude, P_(on)(p) is the on-time ratio, τ_(oη)(ρ) and r_(off) (p)are the lifetime of a bright and a dark state, respectively.
 3. Methodaccording to claim 1, where the magnification of the imaging system isset up as to oversample the point-spread function with the detectorpixels and thus enabling the computation of spatio-temporalcross-cumulants showing improved signal-to-noise ratios as compared totemporal auto-cumulants.
 4. Method according to claim 1 comprising thefollowing steps: Capturing images of blinking point-like emitters with acamera, Transferring and storing these captured images in a memorybuffer, Processing the buffered images from time to time by updating thepartial products p_(s) in which the aggregate values of all capturedimages are accumulated, Each time the previous step is completed,re-evaluating the cumulant

based on ^(˜)P_(s)=P K, where K is the number of yet accumulated images,Displaying an update of

or of derived parameters, Managing and synchronizing the actions of thehard- and software implied in the previous steps, Allowing userinteractions with this control task via a user interface.
 5. Methodaccording to claim 1 for the spectral unmixing of multiple, spectrallydistinct emitter species that fluctuate stochastically andindependently, said method comprising the generation of two or moredetection channels with a distinct spectral response; said method alsocomprising a pre-calibration step consisting in the measurement of theintensity response of the different channels for each species, saidpre-calibration step being followed by multiple combinations of spectralcross-cumulants to unmix the different emitter species by solving alinear equation system.
 6. A microscopy system to be used with themethod as defined in claim 1, said system comprising: A light source,Sample holding means, An illumination arm, A detection arm, A microscopeobjective located on said detection arm and An image or signalprocessing unit processing the sequence of images from blinkingpoint-like emitters and determining said parameter maps and balancedcumulants, A display for displaying said parameter maps and balancedcumulants.
 7. A microscopy system according to claim 6 for probing thefast triplet state fluctuations, involving for example a matchingmodulated excitation scheme comprising pre-pulse activation means topopulate the dark triplet state followed by a short probe pulsesynchronized with the camera exposure or a time-gated detection systemcombined with a synchronized modulation or continuous illuminationscheme; said system furthermore comprising: an excitation modulationdevice in the illumination arm a controller unit driving said excitationmodulation device as well as the camera.
 8. A microscopy systemaccording to claim 6 for inducing stochastic fluctuations externally bythe excitation using a varying structured illumination, said systemfurthermore comprising a device for generating the varying structuredillumination in the object space, for example a varying saturatedspeckle field.
 9. A microscopy system according to the claim 1, whichallows for the simultaneous acquisition of multiple focal planes andconsequently permits spatio-temporal cross-cumulation in 3D, said systemcomprising a dedicated detection arm, for example composed of multiplebeam splitters to split the collected light into multiple detectionchannels, multiple adjustable mirrors with one translational degree offreedom for adjusting distinct optical path lengths in the image spaceand two angular degrees of freedom for directing the channels next toeach other onto at least one array detector; the system furthermorecomprising an additional adjustable field stop, placed at a conjugatedimage plane, to avoid cross talk among the channels.
 10. A microscopysystem to be used with the method of claim 5, said system comprising atleast one spectral beam splitter which generates two or more detectionchannels with a distinct spectral response.